If the values listed on WoWhead are accurate, and assuming you are scrapping pieces you get from other content, you should get a random piece either every week or every other week. Targeting a specific piece will probably take 3-4 weeks, or upwards of 2 months if you are relying solely on M+ cache.

This seems pretty inline with our current rate of getting the piece we want. I’ve been sitting on the same 3 azerite pieces since October. (I’ve received a lot more pieces since then, but none that were an upgrade).